What is the integral from a to 7a of 1/x ?

The integral from a to 7a of 1/x is ln(7)

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integral from a to 7a of 1/x

\int_{a}^{7 a} \frac{1}{x} d x

ln (7)

Decimal

1.94591 \dots

Solution steps

\int_{a}^{7 a} \frac{1}{x} d x

Use the common integral:

\int \frac{1}{x} d x = ln (∣ x ∣)

= [ln ∣ x ∣]_{a}^{7 a}

Compute the boundaries:

ln (7 ∣ a ∣) - ln ∣ a ∣

= ln (7 ∣ a ∣) - ln ∣ a ∣

Simplify

= ln (7)

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\int_{1}^{c o s (x)} 8 t^{7} d t

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\int_{1}^{e} \frac{ln ( x ^{4} )}{x} d x

What is the integral from a to 7a of 1/x ?
The integral from a to 7a of 1/x is ln(7)